code: def testVJPWithVariables(self):
      def f_vjp_fwd(x):
          return x**2 + y**2, x
  
      def f_vjp_bwd(x, dz, variables):
          y = variables[0]
          return 7.0 * dz * x, [7.0 * dz * y]
  
      @custom_gradient.custom_gradient(
          vjp_fwd=f_vjp_fwd,
          vjp_bwd=f_vjp_bwd,
      )
      def f(x):
          return f_vjp_fwd(x)[0]
  
      x = tf.constant(2.0)
      y = tf.Variable(3.0)
      dz = tf.constant(5.0)
  
      self.evaluate(y.initializer)
  
      z1 = f(x)
  
      # Use GradientTape to implicitly capture the variable.
      with tf.GradientTape() as tape:
          tape.watch(x)
          z2 = f(x)
  
      dx, dy = tape.gradient(z2, (x, y), output_gradients=dz)
  
      self.assertAllClose(x**2 + y**2, z1)
      self.assertAllClose(x**2 + y**2, z2)
      self.assertAllClose(7.0 * dz * x, dx)
      self.assertAllClose(7.0 * dz * y, dy)
  
file_path: probability/tensorflow_probability/python/internal/custom_gradient_test.py
imports: import tensorflow.compat.v2
  from tensorflow_probability.python.internal import custom_gradient
  from tensorflow_probability.python.internal import test_util
  from tensorflow_probability.python.math import gradient
label_desc: Use image node_id 2 for calling the CustomGradientTest obj's underlying member method code with example usage: obj.testVJPWithVariables() and returns: unknown,  x, unknown,  list, f_vjp_fwd